$10ef + 3eg - 10e - 7 = 4f - 10$ Solve for $e$.
Combine constant terms on the right. $10ef + 3eg - 10e - {7} = 4f - {10}$ $10ef + 3eg - 10e = 4f - {3}$ Notice that all the terms on the left-hand side of the equation have $e$ in them. $10{e}f + 3{e}g - 10{e} = 4f - 3$ Factor out the $e$ ${e} \cdot \left( 10f + 3g - 10 \right) = 4f - 3$ Isolate the $e$ $e \cdot \left( {10f + 3g - 10} \right) = 4f - 3$ $e = \dfrac{ 4f - 3 }{ {10f + 3g - 10} }$